There’s a stilted, soap opera quality to Hany Khalifa’s “Flight 404,” Egypt’s submission to the Academy Awards. It never quite transcends these visual and narrative trappings, but its tale of a woman escaping her past, en route to her Mecca pilgrimage, is led by a deeply layered performance from Mona Zaki. While the actress brings nuance and fearsome emotional commitment to her role, the film is often restrained by drama so frustratingly opaque that it veers into comical territory.

The diligent Ghada (Zaki) works at an upscale real estate company in Cairo, and makes sure to take breaks for her fajr, or daily Islamic prayer, which doesn’t appear to be a priority for most people around her. However, “Flight 404” is far from the conservative screed such a backdrop might suggest. The plot is set in motion when Ghada’s noon prayers are interrupted by a phone call,...